Get Calculus for Cognitive Scientists: Higher Order Models and PDF

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Extra resources for Calculus for Cognitive Scientists: Higher Order Models and Their Analysis

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There is a lot of ambiguity here as the multiplier x is completely arbitrary. For example,if we let x = 7 c for an arbitrary c, then solving for y, we find y = 2 c. We can then rewrite the solution vector as c 2 7 in terms of the arbitrary multiplier c. It does not really matter what form we pick, however we often try to pick a form which has integers as components. 2 Find all solutions to the consistent system 4x +5y = 0 8 x + 10 y = 0 Solution First, note the determinant of the coefficient matrix of the system is zero.

1. K. 1 (The Inner Product Of Two Vectors) If V and W are two column vectors of size n × 1, the inner product of these vectors is denoted by < V, W > which is defined as the matrix product V T W which is equivalent to the W T V and we interpret this 1×1 matrix product as the real number V1 W1 + V2 W2 + V3 W3 + · · · + Vn Wn where Vi are the components of V and Wi are the components of W . 1 Find the dot product of the vectors V and W given by V = 6 1 and W = 7 . 2 Find the dot product of the vectors V and W given by V = −6 −8 2 .